Since the first work on locally repairable codes in [1]}, [2]}, construction of good locally repairable codes has been a central problem in the study of locally repairable codes [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}.
A locally repairable code is just a block code with an additional parameter called locality.
It was shown in [7]} that the minimum distance \(d(C)\)  of an \([n,k,d]\) -linear code \(C\)  with locality \(r\)  is upper bounded by
\(d(C)\le n-k-\left\lceil \frac{k}{r}\right\rceil +2.\) 
